Define and prove that where θ is the angle between and

Cross Product: The vector or cross product of two non-zero vectors and, denoted by, is defined as



where θ is the angle between and , 0≤θ≤π and is a unit vector perpendicular to both and, such that, and form a right handed system.


We have



is a unit vector




But, we have the dot product of two vectors and forming an angle θ as


Now, we divide these two equations.






Thus,


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